a) Consider an arithmetic series 4+2+0+(-2)+.....i) What is the first term? And find the common difference d.ii) Find the sum of the first 10 terms S(10).b) Solve [tex] {2}^{x - 3} = 7[/tex]
Answers
Answer:
Explanation:
Here, we want to work with an arithmetic series
a) First term
The first term (a) of the arithmetic is the first number on the left
From the question, we can see that this is 4
Hence, 4 is the first term
To find the common difference, we have this as the difference between twwo subsequent terms, going from left to right
We have this as:
[tex]2-4\text{ = 0-2 = -2-0 = -2}[/tex]The common difference d is -2
ii) We want to calculate the sum of the first 10 terms
The formula for this is:
[tex]S(n)\text{ = }\frac{n}{2}(2a\text{ + (n-1)d)}[/tex]Where S(n) is the sum of n terms
n is the number of terms which is 10
a is the first term of the series which is 4
d is the common difference which is -2
Substituting these values, we have it that:
[tex]\begin{gathered} S(10)\text{ = }\frac{10}{2}(2(4)\text{ + (10-1)-2)} \\ \\ S(10)\text{ = 5(8+ (9)(-2))} \\ S(10)\text{ = 5(8-18)} \\ S(10)\text{ = 5(-10)} \\ S(10)\text{ = -50} \end{gathered}[/tex]Related Questions
A parent is buying two types of chocolate truffles for the children. The oldest child likes white chocolate (W), the younger two like dark chocolate (D) and the spouse likes white chocolate (W). Four white chocolate truffles (W) cost the same as three dark chocolate truffles (D). If the parent bought 8 white chocolate truffles(W) and 10 dark chocolate truffles (D), and spent $50.00, how much was each dark chocolate truffle?2.422.343.13
Answers
SOLUTION
Given the information on the question tab;
[tex]Let\text{ the price for a white chocolate truffle be W, and the price for a dark chocolate truffle be D;}[/tex][tex]\begin{gathered} From\text{ the statements made in the question;} \\ 4W=3D-----(1) \\ 8W+10D=50----(2) \end{gathered}[/tex][tex]\begin{gathered} From\text{ equation \lparen1\rparen;} \\ W=\frac{3D}{4}-----(3) \\ substituting\text{ W=}\frac{3D}{4}\text{ into equation \lparen2\rparen} \end{gathered}[/tex][tex]\begin{gathered} 8\times\frac{3D}{4}+10D=50 \\ 6D+10D=50 \\ 16D=50 \\ D=\frac{50}{16} \\ D=3.125\approx3.13 \end{gathered}[/tex]Final answer:
Each dark chocolate truffle costs $3.13
Rewrite the expression in lowest terms.
4x²-12x +9
________
4x2-9
A. -12 x
B. 4x-3
2x-3
C. 2x+3
2x-3
D. 2x-3
2x+3
Answers
answer is D
no real explanation its just math
Which tool would be best to solve this problem?Pythagorean TheoremTriangle Angle Sum TheoremTangent RatioSine RatioCosine RatioUse that tool to solve for x. Show all work on the sketchpad or on your paper.
Answers
To get the value of x,
We use triangle sum theorem:
Triangle Sum Theorem:
The sum of all angles in a triangle is equal to 180 degrees.
In the triangle
We have 90 degree, 22 degree and one x
So,
x + 90 + 22 =180
x + 112 = 180
x = 180-112
x = 68 degree
Answer: x = 68
Solve the right triangle. Write your answers in simplified, rationalized form. DO NOT ROUND!
Answers
base = FG = root 30
perpendicular HG = x
angle = 45 degrees,
we know that
[tex]\text{tan}\theta=\frac{perpendicualr}{base}[/tex][tex]\tan 45=\frac{HG}{\sqrt[]{3}}[/tex][tex]\begin{gathered} 1=\frac{HG}{\sqrt[]{3}} \\ HG=\sqrt[]{3} \end{gathered}[/tex]so, the value of HG = root 3
Trey's chocolate bar is 52% cocoa. If the weight of the chocolate bar is 66 grams, how many grams of cocoa does it contain? Round your answer to the nearest
tenth.
Answers
Trey's chocolate bar is 52% cocoa and if the weight of the chocolate bar is 66 grams, it contains 34.32 grams of cocoa using the concept of percentage.
What is percent?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.What is a fraction?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many parts of a particular size there are when spoken in everyday English.Here, 52% of 66 grams:
=(52/100)*66=0.52*66=34.32 grams of cocoa52% cocoa makes up Trey's chocolate bar.
Using the concept of percentage, a 66-gram chocolate bar would contain 34.32 grams of cocoa.
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help me please im not understanding on the right side it says: to the total number of people present. Express as a simplified ratio
Answers
ANSWER
4 : 9
EXPLANATION
The total number of people present is the number of females plus the number of males:
[tex]125+100=225[/tex]The ratio of number of males to total number of people is:
[tex]\frac{100}{225}[/tex]We have to simplify this fraction. Both 100 and 225 are divisible by 5:
[tex]\begin{gathered} 100\colon5=20 \\ 225\colon5=45 \end{gathered}[/tex]Therefore:
[tex]\frac{100}{225}=\frac{20}{45}[/tex]And then again, 20 and 45 are divisible by 5:
[tex]\begin{gathered} 20\colon5=4 \\ 45\colon5=9 \end{gathered}[/tex]Therefore:
[tex]\frac{100}{225}=\frac{20}{45}=\frac{4}{9}[/tex]We can't simplify more than that, so the ratio is 4 : 9
UsetheprimefactorsmethodtofindtheGCFof76,190,and931.
Answers
There are several ways to calculate the GCF
Let's use the Prime Factorization.
1) List the numbers in a row. As we can see, 76, 190 are both divisible by 2
So le's start dividing by the prime number 2, up to next divisible prime number as it follows:
As we can see the Greatest Common Divisor to both 76,190 and 931 is the prime number 19
Therefore, we can state the GCD of 76,190, 931 as 19
Find the measure of the indicated amgle to the nearest degree.
Answers
The correct option is
C. 69 degrees
Explanation:Let the indicated angle be represented by x, then
[tex]\begin{gathered} \cos x=\frac{Adjacent}{Hypotenuse}=\frac{13}{36} \\ \\ \\ x=\cos^{-1}(\frac{13}{36})\approx69^o \end{gathered}[/tex]Each parking spot is 8 feet wide. A parking lot has 24 parking spots side by side. What is the width (measured in yards) of the parking lot? The shorter tree is
Answers
The width would be: 8ft*24 = 192 ft
Then, we have to convert the unit from ft to yards. Doing so,we have:
[tex]192ft\cdot\frac{1\text{ yard}}{3\text{ ft}}=64\text{ yards (Multiplying and dividing)}[/tex]The answer is 64 yards
Solve using substitution.x = -7-8х - бу = 14
Answers
The given system of equation :
x = - 7
-8x - 6y = 14
Substitute the value of x = (-7) in the given system :
-8x - 6y = 14
-8(-7) - 6y = 14
Simplify the equation :
56 - 6y = 14
56 - 14 = 6y
6y = 42
y = 42/6
y = 7
y = 7 & x = (-7)
Answ
Answer:
Step-by-step explanation:
What is the slope: (-2, 1) (5,-2)
Answers
Answer: slope = -3/7
Step-by-step explanation:
m(slope) = (y2-y1)/(x2-x1)
m = (-2+-1)/(5--2)
m = (-2-1)/5+2)
m = -3/7
Which is the image of vertex K after the parallelogram is rotated 180degrees about the origin?
Answers
Answer:
The image of vertex K is (3,-2)
Step-by-step explanation:
Rotated 180 degrees about the origin means that the value of x will not change, while y will have the same distance from the origin, but in a different direction.
Vertex K:
Value of x: x = 3
Value of y: y = 2
Distance from the origin: 2 - 0 = 2
Rotated, new coordinate: 0 - 2 = -2
The image of vertex K is (3,-2)
1. The population of Whatville is given by the y=83,000(1.04) where x is the years since 2010.a) What was the population in 2010?b) What is the population in 2020?c) When will the population reach 100,000? Show your work.
Answers
ANSWER:
a) 83,000 people
b) 122,860 people
c) 4.75 years
STEP-BY-STEP EXPLANATION:
We have that the population given by the following equation:
[tex]y=83000\cdot\mleft(1.04\mright)^x[/tex]a) What was the population in 2010?
Since no year has passed, the value of x would be 0.
Replacing:
[tex]\begin{gathered} y=83000\cdot(1.04)^0 \\ y=83000 \end{gathered}[/tex]The population in 2010 is 83,000 people
b) What is the population in 2020?
From 2010 to 2020 10 years have passed, therefore the value of x is 10
[tex]\begin{gathered} y=83000\cdot(1.04)^{10} \\ y=122860 \end{gathered}[/tex]The population in 2020 is 122,860 people
c) When will the population reach 100,000?
Since the population is 100,000 people, it is the value of y, therefore we must solve and calculate the value of x
[tex]\begin{gathered} 100000=83000\cdot\mleft(1.04\mright)^x \\ 1.04^x=\frac{100000}{83000} \\ \ln 1.04^x=\ln \frac{100}{83} \\ x\cdot\ln 1.04=\ln \frac{100}{83} \\ x=\frac{\ln \frac{100}{83}}{\ln 1.04} \\ x=4.75 \end{gathered}[/tex]Which means that for the population to be 100,000 people, 4.75 years would have to pass
A circle Is cut from a square piece of cloth as shown How many square inches of cloth are cut from the square 1,061.32in22,122.64in22,704.00in23,622.31in2
Answers
Answer: 2,122.64in².
Explanation
We want to know the measure of the circle in square inches, meaning that we have to calculate the area.
The area of a circle (A) is given by:
[tex]A=\pi r^2[/tex]where r represents the radius of the circle.
The diameter of the circle is a straight line that goes from one point of the circumference of a circle to an opposite point, passing through the center of the circle. The radius is half the diameter.
Based on the image, we can see that the circle is cut touching one point of each side of the square, meaning the diameter is what the side of the square measures:
Then, if the diameter is 52", then the radius is half that, 26".
Now, we can calculate the area:
[tex]A=\pi\cdot26^2[/tex][tex]A=3.14\cdot676[/tex][tex]A=2122.64in^2[/tex]A circle and two distinct lines are drawn on a sheet of paper what is the largest possible number of points of intersection of these figures (it is Q29)
Answers
Answer:
C 5
Step-by-step explanation:
The two lines can both intersect the circle twice, and can intersect each other once, so 2 + 2 + 1 = 5
If mZABD = 70°, what are mZABC and mZDBC?
mZABC=
mZDBC=
(6x+3) D
B
(9x-8)
Please help me
Answers
Answer:
Step-by-step explanation:
ABD = ABC + DBC
Eqivalent to:
78 = (5x + 3) + (5x - 5)
78 = 5x + 5x + 3 - 5
78 = 10x - 2
80 = 10x (move -2 to the left side and get 78 + 2 = 80)
8 = x (80/10 = 8)
With x = 8,
ABC = 5x - 5 = 8*5 - 5 = 40 - 5 = 35
DBC = 5x +3 = 8*5 + 3 = 40 + 3 = 43
what is the curved surface area of a cone on top of a half circle if the cone has a volume and the circle has a 10 area?
Answers
Given a cone with base radius, r, and perpendicular height, h,
the volume, V, is given by
[tex]V=\frac{1}{3}\times\pi\times r^2\times h[/tex]In this case,
r = 10ft,
h = 17ft,
Therefore,
[tex]V=\frac{1}{3}\times\pi\times10^2\times17=\frac{1700}{3}\pi[/tex]Hence, V = 1780.24 cubic feet
The volume of the cone is 1780.24 cubic feet
For these problems, please show your algebraic work using logarithms. 1. Determine the doubling time for each situation listed below. a. A population is growing according to P = P_0e^0.2t b. A bank account is growing by 2.7% each year compounded annually.
Answers
Answer: We need to find the doubling time for population growth:
Population growth is given by
[tex]P=P_oe^{(0.2)t}[/tex]Where:
[tex]\begin{gathered} P\rightarrow\text{final} \\ P_o\rightarrow I\text{nitial} \end{gathered}[/tex]For the population to double, it implies that:
[tex]P=2P_o[/tex]Therefore:
[tex]\frac{P}{P_o}=\frac{2P_o}{P_o}=2=e^{(0.2)t}[/tex]Solving for time "t" gives:
[tex]2=e^{(0.2)t}\rightarrow\ln (2)=(0.2)t\rightarrow t=\frac{\ln (2)}{(0.2)}=3.46u[/tex]Mr. Edmonds is packing school lunches for a field trip for the 6th graders of Apollo Middle school. He has 50 apples and 40 bananas chips. Each group of students will be given one bag containing all of their lunches for the day. Mr. Edmonds wants to put the same number of apples and the same number of bananas in each bag of lunches. What is the greatest number of bags of lunches Mr.Edmonds can make? How many apples and bananas will be in each bag?
Answers
how far a hawk can fly in 15 days
Answers
Answer : 1500 miles
According to the distance time relationship
Distance = Rate x time
From the figure given, the hawk flies 500 miles in 5 days
We can find our rate using the above parameters
Since, distance = rate x time
Rate = distance / time
Rate = 500 / 5
Rate = 100 miles / day
Since, the rate remains constant
How far the hawk can fly in 15 days can be calculated as follows
Time = 15 days
Rate = 100
Distance = ?
Disatnce = rate x time
Distance = 100 x 15
Distance = 1500 miles
The Hawk can fly 1500 miles in 15 days
2. (5 × 2 + 20/2) + (10 x 2/2 + 5) =
a. 35
b. 42
c. 103
Answers
Answer:
a.35
Step-by-step explanation:
10 + 20/2 equals 20
20/2+5 equals 15
20+15 equals 35
NO LINKS!! Please help me with this probability question 3a
Answers
Answer:
b) 26%
Step-by-step explanation:
If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:
[tex]\large\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]
Given:
[tex]\textsf{Mean}\;\mu=3550[/tex]
[tex]\textsf{Standard deviation}\:\sigma=870[/tex]
Therefore, if the weights of the cars passing over the bridge are normally distributed:
[tex]\boxed{X \sim\text{N}(3550,870^2)}[/tex]
where X is the weight of the car.
To find the approximate probability that the weight of a randomly-selected car passing over the bridge is less than 3000 pounds, find[tex]\text{P}(X < 3000)[/tex].
Calculator input for "normal cumulative distribution function (cdf)":
Upper bound: x = 3000Lower bound: x = –9999...μ = 3550σ = 870[tex]\implies \text{P}=0.2636333503[/tex]
[tex]\implies \text{P}=26\%[/tex]
Therefore, the approximate probability that the weight of a randomly-selected car passing over the bridge is less than 3000 pounds is 26%.
The graph shows the proportional relationship between the number of gems collected and the number of levels that have been completed in a video game.
Graph with x axis labeled game levels and y axis labeled gems collected. A line begins at 0 comma 0 and goes through points 6 comma 420 and 8 comma 560.
Determine the constant of proportionality for the relationship.
p = 70
p = 140
p equals 2 over 140
p = 0.0143
Answers
Answer: P = 70
Step-by-step explanation:
p = 70 because on the graph everytime the y number is the x number multiplied by 70.
70 x 2 = 140
70 x 4 = 280
70 x 6 = 420
70 x 8 = 560
70 x 10 = 700.
Heres the chart for proof
The constant of proportionality (p) for this proportional relationship is equal to: A. p = 70.
How to determine the constant of proportionality?In Mathematics, the graph of any proportional relationship is characterized by a straight line because as the values on the x-axis increases or decreases, the values on the y-axis increases or decreases simultaneously.
Mathematically, a proportional relationship can be represented by the following equation:
y = px
Where:
p is the constant of proportionality.y represents the gems collected.x represents the game levels.Next, we would determine the constant of proportionality (p) for the data points on this graph as follows:
p = y/x
p = 420/6 = 560/8
p = 70.
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In a data set, the median is less than the mean. What does that indicate about the data?A.It is skewed to the right.B.It is skewed to the left.C.It is symmetric.D.It is bell-shaped.
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
In a data set, the median is less than the mean. What does that indicate about the data?
A. It is skewed to the right.
B. It is skewed to the left.
C. It is symmetric.
D. It is bell-shaped.
Step 2:
The diagram that explains the question above is:
A left-skewed distribution has a long left tail. Left-skewed distributions are also called negatively-skewed distributions. That’s because there is a long tail in the negative direction on the number line. The mean is also to the left of the peak.
A right-skewed distribution has a long right tail. Right-skewed distributions are also called positive-skew distributions. That’s because there is a long tail in the positive direction on the number line. The mean is also to the right of the peak.
Back to the question, in a data set, the median is less than the mean
It indicates that:
It is skewed to the right ( OPTION A )
This is due tomorrow! Smart people help me, please!!
Answers
The table represents the amount of money in a bank account each month. Month Balance ($) 1 2,215.25 2 2,089.75 3 1,964.25 4 1,838.75 5 1,713.25 What type of function represents the bank account as a function of time? Justify your answer.
Answers
The type of function that represents the bank account as a function of time is a linear function
How to determine the type of function?The table of values is given as
Month Balance ($)
1 2,215.25
2 2,089.75
3 1,964.25
4 1,838.75
5 1,713.25
From the above table of values, we can see that;
The balance in the bank account reduces each month by $125.5
This difference is calculated by subtracting the current balance from the previous balance
So, we have
Difference = 1,838.75 - 1713.25 =125.5
Difference = 1,964.25 - 1,838.75 =125.5
Difference = 2,089.75 - 1,964.25 =125.5
Difference = 2,215.25 - 2,089.75 =125.5
Functions that have a common difference are linear functions
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Answer:
It's not D I can tell you that but ig just go with the other guy's answer
Step-by-step explanation:
What is the volume of the cone rounded to the nearest tenth? The diagram is not drawn to scale. The height of the cone is 19 yd.A) 2646.3 yd^3B) 1462.4 yd^3C) 1039.0 yd^3D) 975.0 yd^3
Answers
Answer:
To find the volume of the cone rounded to the nearest tenth
we have that,
Volume of the cone (V) is,
[tex]\frac{1}{3}\pi r^2h[/tex]where r is the radius and h is the height of the cone.
Given that,
r=7 yd
h=19 yd
Substitute the values we get,
[tex]V=\frac{1}{3}\pi(7)^2\times19[/tex]we get,
[tex]V=\frac{931}{3}\pi[/tex]we know that pi is approximately equal to 3.14, Substitute the value we get,
[tex]V=\frac{931}{3}(3.14)[/tex]we get,
[tex]V=974.446\approx975\text{ yd}^3[/tex]Answer is: Option D:
[tex]\begin{equation*} 975\text{ yd}^3 \end{equation*}[/tex]A line's slope is -5. The line passes through the point (5, 30). Find an equation for this line in both point-slope and slope-intercept form A) An equation for this line in point-slope form is:B) An equation for this line in slope-intercept form is.
Answers
Answer:
y - 30 = 5(x - 5) (point slope form)
slope intercept form is y = 5x+5
Explanation:
Given the following
Slope m = -5
Point = (5, 30)
x0 = 5 and y= = 30
The equation of the line in point slope form is expressed as y-y0 = m(x-x0)
Substitute
y - 30 = -5(x - 5) (point slope form)
Express in slope intercept form (y = mx+c)
y - 30 = -5x + 25
y = -5x + 25 + 30
y = -5x + 55
Hence the equation of the line in slope intercept form is y = -5x+55
The length is twice the sum of its width 3. What are the dimension of the rectangle if it’s area 216 square inches?
Answers
Assume that the width of the rectangle = x
Since the length is twice the sum of the width and 3, then
[tex]\begin{gathered} L=2(x+3) \\ L=2x+6 \end{gathered}[/tex]Since the area of the rectangle is 216 square inches, then
Multiply the length and the width, then equate the product by 216
[tex]\begin{gathered} (x)(2x+6)=216 \\ 2x^2+6x=216 \end{gathered}[/tex]Divide all terms by 2 to simplify
[tex]\begin{gathered} \frac{2x^2}{2}+\frac{6x}{2}=\frac{216}{2} \\ x^2+3x=108 \end{gathered}[/tex]Subtract 108 from both sides
[tex]\begin{gathered} x^2+3x-108=108-108 \\ x^2+3x-108=0 \end{gathered}[/tex]Now, let us factorize the trinomial into 2 factors
[tex]\begin{gathered} x^2=(x)(x) \\ -108=(-9)(12) \\ (x)(-9)+(x)(12)=-9x+12x=3x \end{gathered}[/tex]Then the factors are
[tex]x^2+3x-108=^{}(x-9)(x+12)[/tex]Equate them by 0
[tex](x-9)(x+12)=0[/tex]Equate each factor by 0, then find the values of x
[tex]x-9=0[/tex]Add 9 to both sides
[tex]\begin{gathered} x-9+9=0+9 \\ x=9 \end{gathered}[/tex][tex]x+12=0[/tex]Subtract 12 from both sides
[tex]\begin{gathered} x+12-12=0-12 \\ x=-12 \end{gathered}[/tex]Since the width can not be a negative number (no negative length)
Then the width of the rectangle = 9
Let us find the length
[tex]\begin{gathered} L=2(9)+6 \\ L=18+6 \\ L=24 \end{gathered}[/tex]Then the dimensions of the rectangle are 9 inches and 24 inches
Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers
Answers
Explanation
Let's remember some properties ofthe fractions ans exponents,
[tex]\begin{gathered} a^{-n}=\frac{1}{a^n} \\ (\frac{a}{b})^n=\frac{a^n}{b^n} \\ (ab)^n=a^nb^n \\ (a^n)^m=a^{m\cdot n} \end{gathered}[/tex]so
Step 1
[tex]\lbrack\frac{4p^{-2}q}{3^{-1}m^3}\rbrack^2[/tex]reduce by using the properties
[tex]\begin{gathered} \lbrack\frac{4p^{-2}q}{3^{-1}m^3}\rbrack^2 \\ \lbrack\frac{4q}{3^{-1}m^3p^2}\rbrack^2 \\ \lbrack\frac{3^1\cdot4q}{m^3p^2}\rbrack^2 \\ \lbrack\frac{12q}{m^3p^2}\rbrack^2 \\ \lbrack\frac{144q^2}{m^{3\cdot2}p^{2\cdot2}}\rbrack^{} \\ \lbrack\frac{144q^2}{m^6p^4}\rbrack^{} \end{gathered}[/tex]therefore, the answer is
[tex]\lbrack\frac{144q^2}{m^6p^4}\rbrack^{}[/tex]I hope this helps you